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There are several goodness of fit tests, may be chi-squared is most famous one, however it seems it is not a preferable choice to be used in the case of continous variables. There is an excellent discussion here: Goodness-of-Fit for continuous variables

I wonder is there any specific suggestion in of normal distribution:

Question: What criteria to use for goodness-of-fit test for normal distribution ?

Alexander Chervov
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    [This answer](https://stats.stackexchange.com/a/76384/17230) gives good advice on normality testing. If testing is appropriate, the choice of test depends rather on the kind of departure from normality you're interested in picking up. – Scortchi - Reinstate Monica Jun 26 '18 at 12:23
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    I'd also suggest reading [Is normality testing essentially useless?](https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless/); in particular, if you're testing *assumptions* of some other procedure, I'd point you to [Harvey Motulsky's answer](https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless/2501#2501) there. If you have a good reason to test normality (there aren't many of those but they do come up sometimes), then there are some tests with fairly good power against a range of alternatives, ... ctd – Glen_b Jun 26 '18 at 12:35
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    ctd... (the Shapiro-Wilk is popular, and a perfectly good choice, though the Chen-Shapiro is a bit better vs a fair number of alternatives) but if you have specific alternatives you want to be sure you have good power against, it's best to tailor the choice of test toward them. – Glen_b Jun 26 '18 at 12:35

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